Geometry 2022

Lecturer: Roland van der Veen, assistants: Boudewijn Bosch, Bram Brongers and Oscar Koster.

This course is meant to introduce various types of geometry, roughly divided into three parts: Euclidean, projective and differential geometry. For a longer description of the course see the Ocasys page.

Organisation: The lectures will be live and also recorded on Nestor.

In addition we will make active use of the Nestor discussion board, will you join us there? Posting a question on the discussion board is useful for at least four reasons: 1) Making the effort to formulate your question helps solving it. 2) You may get an answer 3) it helps building a community and promotes interaction 4) You get bonus points (see below).

Assessment: Regular homework sets and a written exam. Homework should be uploaded to Nestor before class on the Tuesday after it was announced. Homework is compulsory and should be handed in using the Nestor environment. It counts as 25% of the total grade, written exam counts for 75%. The homework grade is computed as the average of the 6 best sets handed in. Active participation on the Euclidean Connection forum in the first four weeks can earn you up to a full bonus point on your homework grade. In the final four weeks you can again earn a full point on your homework grade so in theory you could get a 12 for your homework. Some of the homework assignments may ask you to upload a short video where you explain your work.

Literature: We will work through the lecture notes specifically written for this course.

Schedule

1: Week of Feb. 7 Euclidean geometry: polytopes, simplices, angles.
Tutorial exercises:
Differential geometry: Spherical and hyperbolic geometry.
Tutorial exercises:
2: Week of Feb. 14 Projective geometry: Perspective drawing, linear algebra.
Tutorial exercises:
Differential geometry: Riemannian metric, lengths, angles.
Tutorial exercises:
3: Week of Feb. 21 Projective geometry: Projective spaces, plines, pplanes and homogeneous coordinates.
Tutorial exercises:
Differential geometry: Riemannian pull-back metrics, area polytopes, simplices, angles.
Tutorial exercises:
4: Week of Feb. 28 Euclidean geometry:Euclidean isometries, rotation, reflection, translation.
Tutorial exercises:
Differential geometry: Variational principle, isometries
Tutorial exercises:
5: Week of Mar. Euclidean geometry: Eucl. Isometries structure of Euclidean group.
Tutorial exercises:
Differential geometry: Christoffel symbols, geod equation.
Tutorial exercises:
6: Week of Mar. Euclidean geometry:Simpl complexes Euler char., homology
Tutorial exercises:
Projective geometry: Quadrics and conics
Tutorial exercises:
7: Week of Mar. Euclidean geometry: holes and homology
Tutorial exercises:
Differential geometry: Geodesics.
Tutorial exercises:
8: Week of Mar. Euclidean geometry: Quaternions, homology
Tutorial exercises:
Projective geometry: Projective duality
Tutorial exercises:

Links

Computer/Mathematica resources